I need to estimate the mean and variance of three variables. One is continuous and bounded between -100 and 100; the second is continuous and bounded between 1 and 10; the third is discrete and bounded between 1 and 10.
The mean of a variable may be near one of the bounds. If so, how can I take advantage of that information in constructing smaller confidence intervals for the mean (and variance)?
The ideal set of deliverables is described below. But I may be willing to accept a subset or alternatives. Please propose what you can do as well as an estimate of the range of labor hours needed to produce.
Desired Deliverables (in order of priority):
1. Theoretical explanation of how to solve the problem. Brief is better. Tell me how many pages I'll have to read. You can assume I already understand confidence intervals for unbounded continuous variables.
2. Formulas for estimating needed sample size and for calculating confidence intervals.
3. Adjustments in the above for sampling from a finite population.
4. Computer code for implementing the formulas (R, SPSS, Minitab, or SAS Base ... listed in order of preference)
Less than 30 hrs/week
Less than 1 month< 1 monthProject LengthDuration
I am looking for a mix of experience and value